the shape of (new) physics in b decays - unam...hierarchyin the mixing of the quark ﬂavor...

The shape of (new) physics in B decays

J. Martin Camalich

FLASY2015

June 30, 2015

The flavor puzzle of the Standard Model

The standard model explains very successfully flavor transitions

However it does not explain . . .

3 families

Hierarchy of the masses of the fermions

Hierarchy in the mixing of the quark flavor

Anarchy in the mixing of the lepton flavor

Answering these questions require physics beyond the SM

J. Martin Camalich (UCSD) (News) in B-physics June 30, 2015 2 / 26

Ben Grinstein’s talkJ. Martin Camalich (UCSD) (News) in B-physics June 30, 2015 3 / 26

No New Physics at colliders (yet?) (Similar plots for ATLAS)

https://twiki.cern.ch/twiki/bin/view/CMSPublic/ https://twiki.cern.ch/twiki/bin/view/AtlasPublic/

CMS Exotica Physics Group Summary – Moriond, 2015

stopped gluino (cloud)stopped stop (cloud)HSCP gluino (cloud)

HSCP stop (cloud)q=2/3e HSCP

q=3e HSCPchargino, ctau>100ns, AMSB

neutralino, ctau=25cm, ECAL time

0 1 2 3 4

RS1(γγ), k=0.1RS1(ee,μμ), k=0.1

RS1(jj), k=0.1RS1(WW→4j), k=0.1

0 1 2 3 4

coloron(jj) x2coloron(4j) x2

gluino(3j) x2gluino(jjb) x2

0 1 2 3 4

RS Gravitons

Multijet Resonances

Long-Lived Particles

SSM Z'(ττ)SSM Z'(jj)

SSM Z'(bb)SSM Z'(ee)+Z'(µµ)

SSM W'(jj)SSM W'(lv)

SSM W'(WZ→lvll)SSM W'(WZ→4j)

0 1 2 3 4

Heavy Gauge Bosons

CMS Preliminary

j+MET, vector DM=100 GeV, Λj+MET, axial-vector DM=100 GeV, Λ

j+MET, scalar DM=100 GeV, Λγ+MET, vector DM=100 GeV, Λ

γ+MET, axial-vector DM=100 GeV, Λl+MET, ξ=+1, SI/SD DM=100 GeV, Λl+MET, ξ=-1, SI/SD DM=100 GeV, Λl+MET, ξ=0, SI/SD DM=100 GeV, Λ

0 1 2 3 4

Dark Matter

LQ1(ej) x2LQ1(ej)+LQ1(νj)

LQ2(μj) x2LQ2(μj)+LQ2(νj)

LQ3(νb) x2LQ3(τb) x2LQ3(τt) x2LQ3(vt) x2

Single LQ1 (λ=1)Single LQ2 (λ=1)

0 1 2 3 4

Leptoquarks

e* (M=Λ)μ* (M=Λ)

q* (qg)q* (qγ)

b*0 1 2 3 4

Excited Fermions dijets, Λ+ LL/RR

dijets, Λ- LL/RRdimuons, Λ+ LLIMdimuons, Λ- LLIM

dielectrons, Λ+ LLIMdielectrons, Λ- LLIM

single e, Λ HnCMsingle μ, Λ HnCMinclusive jets, Λ+inclusive jets, Λ-

0 1 2 3 4 5 6 7 8 9 101112131415161718192021

ADD (γ+MET), nED=4, MDADD (j+MET), nED=4, MDADD (ee,μμ), nED=4, MS

ADD (γγ), nED=4, MSADD (jj), nED=4, MS

QBH, nED=4, MD=4 TeVNR BH, nED=4, MD=4 TeV

QBH (jj), nED=4, MD=4 TeVJet Extinction Scale

String Scale (jj)

0 1 2 3 4 5 6 7 8 9

Large Extra Dimensions

Compositeness

TeV

TeV

TeV

TeV

TeV

TeV

TeV

TeV

TeV


Lepton universality violation in B decays?“RK anomaly” in B → K `` (FCNC)! LHCb PRL113(2014)151601

Tension with SM ∼2.6σOther anomalies in b → sµµ

I Branching fractions B → Kµµ, Bs → φµµI Angular analysis B → K∗µµ

Up to 4σ in global fitsAltmannshofer and Straub ’14

“RD(∗) anomaly” in B → D(∗)`ν! (CC)

T. Kuhr (Belle) @ FPCP2015

Excesses observed at more than 4σ

T. Freytsis et al. 1506.08896


Effective field theory approach to b → s`` decays

CC (Fermi theory):b sWL L

c c

⇒ GF Vcb V ∗cs C2 c̄LγµbL s̄LγµcLFCNC:b

t

s

γ

WR L

t

b s

γ

R L

W

t

⇒ e4π2

GF Vtb V ∗ts mb C7 s̄LσµνbR Fµν

b

t

sWL L

t

Z, γ

l l

b sL L

Z, γ

l l

W

tb sL L

ll

t

W

ν

⇒ GF Vtb V ∗tsα

4πC9(10) s̄Lγ

µbL ¯̀γµ(γ5)`

I Wilson coefficients Ck (µ) calculated in P.T. at µ = mW and rescaled to µ = mb

K∗B

d

b s

l

lI Light fields active at long distances

Nonperturbative QCD!F Factorization of scales mb vs. ΛQCD

HQEFT, QCDF, SCET,. . .


Effective field theories: Bottom-up approach to new physics

Guiding principleConstruct the most general effective operators Ok made of φ ∈ u, d , s, c, b, l, ν,Fµνand subject to the strictures of SU(3)c × U(1)em

New physics manifest at the operator level through. . .I Different values of the Wilson coefficients Cexpt.i = C

SMi + δCi

I New operators absent or very suppressed in the SMF New chirally-flipped operators

O′7 =4GF√

2

e4π2

m̂b s̄σµνPLFµνb; O′9(10) =

4GF√2

α

4πs̄γµPRb ¯̀γµ(γ5)`

F 4 new scalar and pseudoscalar operators

O(′)S =4GF√

2

α

4π(s̄PR,Lb) (¯̀`); O

(′)P =

4GF√2

α

4π(s̄PR,Lb) (¯̀γ5 `)

F 2 new tensor operators

OT (5) =4GF√

2

α

4π(s̄σµνb) (¯̀σµν(γ5)`).

I The Wilson coefficients can be complex and introduce new sources of CP/


But hold on. . .I No evidence of new-particles on-shell at colliders up to E ' 1 TeV. . .

. . . except a scalar at s ' 125 GeV that very much resembles the SM Higgs

Guiding principle (rewritten)Construct the most general effective operators Ok built with all the SM fields andsubject to the strictures of SU(3)c × SU(2)L × U(1)Y

Buchmuller et al.’86,Grzadkowski et al.’10

For scalar and tensor operators Γ = I, σµν we only have:1

Λ2(ēR Γ `aL)︸︷︷︸

Y =1/2

(q̄aL Γ dR)︸︷︷︸Y =−1/2

1Λ2εab (¯̀bL Γ eR)︸︷︷︸

Y =−1/2

(q̄aL Γ uR)︸︷︷︸Y =1/2

Furthermore:(d̄jσµνPRdi )(¯̀σµνPL`) = 0

Constraints in b → s`` up to O(v2/Λ2)I From 4 scalar operators to only 2!

I From 2 tensor operators to none!Alonso, Grinstein, JMC, PRL113(2014)241802


B0q → ``

Bq

l

l

Z

b

q

CMS and LHCb combined arXiv: 1411.4413

]2c [MeV/−µ+µm5000 5200 5400 5600 5800

)2 cC

andi

date

s / (

40 M

eV/

0

2

4

6

8

10

12

14

16

Data

Signal and background−µ+µ →s

0B−µ+µ →0B

Combinatorial bkg.

Semileptonic bkg.

Peaking bkg.

CMS and LHCb (LHC run I)

Bsl 'G2F

64π3τBs m

3Bs fBs |VtbV

∗ts |2 ×

{|CS − C′S |2 + |CP − C′P + 2

mlmBs

(C10 − C′10)|2}

Decay is chirally suppressed: Very sensitive to (pseudo)scalar operators!

Semileptonic decay constants fBq can be calculated in LQCDFLAG averages Eur.Phys.J. C74 (2014) 2890

Updated predictions:Bobeth et al. PRL112(2014)101801 BSMsµ = 3.65(23)×10−9

Bexptsµ = 2.9(7)× 10−9


Phenomenological consequences Bq → ``

Rql =Bql(Bql)

SM

=1 +All∆Γ yq

1 + yq

(|S|2 + |P|2

),

De Bruyn et al. ’12

S =

√1−

4m2lm2Bq

m2Bq2ml

CS − C′S(mb + mq)CSM10

, P =C10 − C′10

CSM10+

m2Bq2ml

CP − C′P(mb + mq)CSM10

Bq → `` blind to the orthogonal combinations CS + C′S and CP + C′PScalar operators unconstrained!


Phenomenological consequences Bq → ``

Rql =Bql(Bql)

SM

=1 +All∆Γ yq

1 + yq

(|S|2 + |P|2

),

S =

√1−

4m2lm2Bq

m2Bq2ml

CS − C′S(mb + mq)CSM10

, P =C10 − C′10

CSM10−

m2Bq2ml

CS + C′S(mb + mq)CSM10

ΛNP (95%C.L.) RGE of QCD+EW+Yukawas

Channels sµ dµ se deC(′)S (mW ) 0.1 0.15 0.6 1.5Λ [TeV] 79 130 36 49

Alonso, Grinstein, JMC, PRL113(2014)241802


Phenomenological consequences: B → K ``

KB

d

b s

l

l

LHCb JHEP06(2014)133, JHEP05(2014)082,PRL111 (2013)112003,. . .

dΓdq2

=G2F α

2|VtbV ∗ts |2

1536π5f 2+

(|C9 + C′9 + 2

TKf+|2 + |C10 + C′10|2

)+O( m

4`

q4)

Phenomenologically richer (3-body decay)I Decay rate is a function of dilepton invariant mass q2 ∈ [4m2` , (mB −mK )

2]I 1 angle: Angular analysis sensitive only to scalar and tensor operators

Bobeth et al., JHEP 0712 (2007) 040

However: Very complicated nonperturbative problemI 3 hadronic form factors (q2-dependent functions)I “Non-factorizable” contribution of 4-quark operators+EM current


Phenomenological consequences: B → K ``Then in the SM for q2 & 1 GeV2

RK ≡Br(B+ → K +µ+µ−

)Br (B+ → K +e+e−) = 1 +O(10

−4)

The RK anomaly

〈RK 〉[1,6] = 0.745+0.090−0.074(stat)± 0.036(syst)

LHCb, Phys.Rev.Lett.113(2014)151601

2.6σ discrepancy with the SM 〈RK 〉[1,6] = 1.0003(1)SU(2)L × U(1)Y :

I No tensorsI Scalar operators constrained by Bs → `` alone:

RK ∈ [0.982, 1.007] at 95% CL

The effect must come from O(′)9,10RK ' 0.75 for δCµ9 = −δC

µ10 = −0.5

Alonso, Grinstein, JMC, PRL113(2014)241802


B̄ → K̄ ∗`+`−

K∗B

d

b s

l

l

CDF 100 PRL106(2011)161801

BaBar 150 PRD86(2012)032012

Belle 200 PRL103(2009)171801

CMS 400 PLB727(2013)77

ATLAS 500 arXiv:1310.4213

LHCb (µ) 3000 (3 fb−1) LHCb-CONF-2015-002LHCb (e) 128 ([0.0004, 1] GeV2) JHEP 1504(2015)064

4-body decay

d(4)Γdq2 d(cos θl )d(cos θk )dφ

= 932π (Is1 sin

2 θk +Ic1 cos

2 θk

+ (Is2 sin2 θk +I

c2 cos

2 θk ) cos 2θl +I3 sin2 θk sin

2 θl cos 2φ

+ I4 sin 2θk sin 2θl cosφ+I5 sin 2θk sin θl cosφ+I6 sin2 θk cos θl

+ I7 sin 2θk sin θl sinφ+I8 sin 2θk sin 2θl sinφ+I9 sin2 θk sin2 θl sin 2φ)


Large-recoil region (low q2)I Heavy to collinear light quark⇒ QCDf or SCET (power-corrections)I Dominant effect of the photon pole

Charmonium regionI Dominated by long-distance (hadronic) effectsI Starting at the perturbative cc̄ threshold q2 ' 6− 7 GeV2

Low-recoil region (high q2)I Heavy quark EFT + Operator Product Expansion (OPE) (duality violation)I Dominated by semileptonic operators


The P ′5 anomaly at low q2 (1 fb−1)

δCµ9 ' −1Descotes-Genon et al. PRD88,074002

Altmannshofer et al. Eur.Phys.J. C73 (2013) 2646

Consistent with RK !Alonso, Grinstein, JMC, PRL113(2014)241802


The P ′5 anomaly: New Physics?

QUESTION: Do we really understand the hadronic effects?


Connecting theory to experiment: The helicity amplitudes

Helicity amplitudes λ = ±1, 0

HV (λ) = −iN{

C9ṼLλ −m2Bq2[2 m̂b

mBC7T̃Lλ − 16π2hλ

]},

HA(λ) = −iNC10ṼLλ, HP = iN2 mlm̂b

q2C10(

S̃L +msmb

S̃R)

C9 is exposed to various hadronic backgroundsHadronic form factors7 independent q2-dependent nonperturbative functionsBharucha et al.JHEP 1009 (2010) 090, Jäeger and JMC JHEP1305(2013)043

“Non factorizable” contribution

hλ ∝∫

d4yeiq·y 〈K̄ ∗|jem,had,µ(y)Hhad(0)|B̄〉�∗µ

Calculable in QCDf at q2 . 6 GeV2

Beneke et al.’01


Analysis of the angular observables of B → K ∗µµ with 1 fb−1

Use only EFT for QCD (SCET)+model independent constraintsJäger and JMC, arXiv:1412.3183

LHCb just released preliminar angular analysis with 3 fb−1 LHCb-CONF-2015-002

3.6σ using “QCD form factors” (LCSRs)

Ongoing (QCD) model-independent analysis

Effect depends on q2? Straub at Moriond’15Stay tuned! Turbulences ahead!


The shape of the (new) physics

Let’s assume RK and P ′5 are NP

δCµ9 = −δCµ10 = −0.5

δCe9 = δCe10 = 0

Hiller and Schmaltz’14, Straub et al’14’15, Ghosh et al’14,. . .

Only 2 dim-6 SU(2)L × U(1)Y -invariant operators

Q(1)`q =1

Λ2(q̄LγµqL)(¯̀L γµ`L) Q

(3)`q =

1Λ2

(q̄L γµ~τqL) · (¯̀L γµ~τ`L)

1 Lepton Universality Violation⇒ Lepton flavor Violation?2 Operators with SU(2)L quark doublets

I FCNC with neutrinos and/or up quarksI V − A Contributions CC (b → c`ν̄, t → b ¯̀ν. . . )


Lepton flavor symmetries in the SM

SU(3)` × SU(3)e × U(1)L × U(1)e−` , `L ∼ (3, 1)1,−1 , eR ∼ (1, 3)1,1

Broken only by the Yukawas in the SM

−LY ⊃ �e ¯̀LŶeeRH + h.c., (Ye=�e Ŷe, tr(Ŷe Ŷ†e )=1)

U(1)τ × U(1)µ × U(1)e survives

However: Any new source of flavor violation will lead to LF violation. . .Glashow et al. PRL114(2015)091801, Bhattacharya et al. arXiv:1505.04692, Lee et al. arXiv:1505.04692



SU(3)` × SU(3)e × U(1)L × U(1)e−` , `L ∼ (3, 1)1,−1 , eR ∼ (1, 3)1,1





LFV in b → s``′!!

Boucenna et al. arXiv:1503.07099



SU(3)` × SU(3)e × U(1)L × U(1)e−` , `L ∼ (3, 1)1,−1 , eR ∼ (1, 3)1,1





. . . unless it is “aligned” with the Yukawas (e.g. Crivellin et al. PRL114(2015)151801, Celis et al. arXiv:1505.03079)

Minimal flavor violationThe only source of lepton flavor structure in the new physics are the YukawasChivukula et al’87s, D’Ambrosio et al’02, Cirigliano et al’05

Introduce spurions Ŷe ∼ (3, 3̄) and �e ∼ (−1, 1)

Alonso, Grinstein and JMC arXiv:1505.05164


LNP= 1Λ2

[(q̄′L C

(1)q γ

µq′L)( ¯̀′L Ŷe Ŷ

†e γµ`

′L)+(q̄

′L C

(3)q γ

µ~τq′L)·( ¯̀′L Ŷe Ŷ

†e γµ~τ`

′L)]

Hierarchic leptonic couplings (no LFV)

Interactions ∼ δαβm2α/m2τ1 Boost of 103 in b → sττ !

B(B → K τ−τ+) ' 2× 10−4, B(B+ → K +ττ)expt < 3.3× 10−3

2 Very strong constraint from b → sντντ3 Sizable effects in CC tauonic B decays!

RD(∗) =B(B̄→D(∗)τν̄τ )B(B̄→D(∗)µν̄µ)

I Excess observed at more than 4σ

SM Expt.RD 0.300(10) 0.388(47)RD∗ 0.252(5) 0.321(21)

I ΛNP ' 3 TeV

Alonso et al. arXiv:1505.05164


Survey of leptoquark models

Scalar LQ

L∆=(y`u ¯̀L uR +yeq ēR iτ2 qL) ∆−7/6

+y`d ¯̀L dR ∆−1/6+(y`q ¯̀cL iτ2 qL+yeu ēcR uR) ∆1/3

+yed ēcR dR ∆4/3+y

′`q

¯̀cL iτ2~τqL ·~∆

′1/3

Vector LQ

LV =(g`q ¯̀LγµqL+ged ēRγµdR) Vµ−2/3

+geu ēRγµuR Vµ5/3+g

′`q

¯̀Lγµ~τqL ·~V′µ−2/3

+(g`d ¯̀LγµdcR +geq ēRγµqcL) V

µ−5/6+g`u

¯̀LγµucR V

µ1/6

Büchmuller and Wyler’87, Davidson et al.’94,. . .

Assume MLQ � v : Only Vµ−2/3 can work with (our) MFV! Alonso et al. arXiv:1505.05164


Dressing the chosen one . . .

∆LV =(

gq ¯̀LŶeγµqL + gd ε∗e ēRγµdR)

Vµ−2/3 + h.c.

Davidson et al. JHEP 1011 (2010) 073, Grinstein et al. JHEP 1011 (2010) 067, Alonso et al. arXiv:1505.05164

Vµ−2/3 flavored under SU(3)` × SU(3)e × U(1)L × U(1)`−eI Vµ−2/3 ∼ (3, 1)1,−1I g iq , i ≡ d , s, b vector in quark-flavor spaceI gd contribution naturally suppressed by |εe|

b → sµµ anomalies

αeπλtsδCµ9 = −

v2

M2

(mµmτ

)2(gsq)

∗gbq

Hiller et al. PRD90(2014)054014, Gripaios

et al. JHEP1505(2015)006, Sahoo et al. PRD91(2015)094019,

Medeiros Varzielas et al arXiv:1503.01084, Becirevic

et al. arXiv:1503.09024

Tauonic charged currents

�kj,τL =12

v2

M2∑

k

VikVij

(gkq )∗g jq

Sakaki et al. PRD88(2013)9,094012, arXiv:1412.3761


Collider constraints

PRL110(2013)081801, PLBB739 (2014)229 . . . JHEP 1306 (2013) 033, . . .

CMS Searched for vector (scalar) LQs using 4.8 fb−1 (19.7 fb−1)

Vector LQs with 1/2 coupling to τ b: MLQ & 600 GeV at 95% CL


LQ mass set at MLQ = 750 GeV

Perturbativity bound: g iq 6√

4π

Interplay between LHC searches ,FCNC and CC b decays

Can be tested model-independently with top decays

Lc.c.⊃−GF Vtb√

2(1+�tbL )(b̄ γ

µtL) (ν̄Lγµτ) with �tb,τL '

12

v2

M2 |gbq |2

CDF measured Rtτ = Γ(t→τνq)Γ(t→τνq)SM < 5.2 at 95% C.L. PLB639(2006)172

Semileptonic top decays correlated with LUV anomalies!

Discussion of Z ′ models: Avelino’s talk


Conclusions

1 EFT approach very efficient method to investigate anomaliesI Connect low- and high-energy information in a systematic fashionI Constraints between low-energy operators

F 2 out of 4 independent scalar operators and no tensors in di → dj``

2 The b → s`` anomaliesI Bq → ``I RK in B → K ``I The P′5 anomaly in B → K

∗µµ

3 The shape of new physicsI Left-handed-left-handed scenario seems favoredI LFV or MLFV? Both scenarios have testable consequencesI Impact on charged current tauonic B decays: The RD(∗) anomalies

With the LHC run2 very exciting times ahead!


Flavor puzzle of the standard model and new physicsThe effective way of lifeThe bs anomaliesBqBKBK*

The shape of new physicsLepton flavor violation vs. minimal flavor violationApplications to model-building: LQs in MFV scenarios

the shape of (new) physics in b decays - unam...hierarchyin the mixing of the quark ﬂavor...

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